任意结构形状的电容传感器原理和数学模型

在木材工业中，木材含水率检测应用的单一平面电容传感器都是采用大量实验或近似数学模型实现检测的，难以控制和分析误差。鉴于此，并根据木材的介电常数与其含水率存在着一一对应的关系，该文研究了用于测量介电常数、具有任意几何结构形状的电容传感器。利用静电场及静电场中的导体和电介质的性质等相关理论，在电极和被测物处于任意几何结构形状和任意空间相对位置的状态下，建立了测量介电常数的电容传感器的精确数学模型。以经典物理学中已知结果的球形电容传感器为算例，得到了与传统电磁场理论中完全一样的结果，验证了所建立数学模型的正确性。 

The working principles and mathematical model of the capacitive sensor with electrodes of arbitrary shape

In wood industry, based on massy experimental data or approximately mathematical models, single planar capacitance sensors have been used for measuring wood moisture content and are consequently difficult to error analysis and control. In view of a solution to these problems and a corresponding relationship between function value of dielectric constant and moisture content, a systematic research was conducted on the capacitive sensor with electrodes of arbitrary shape used for the measurement of dielectric constants. In accordance with theories of electrostatic field and the characters of conductors and dielectrics were the field, an exactly mathematical model of the sensor was established for the measurement of dielectrics when electrodes and dielectrics were in arbitrary shapes and in randomly relative positions. In the case of spherical capacitor, which was used as the example of analysis, the result was the same as that from the original theories of classical electromagnetics and confirmed the validity of the mathematical model. The research result provides a foundation of the exactly numerical solution for the single planar capacitance sensors used in the wood moisture content measurement.